# How to evaluate avg speed at which a driver approaches curve

## Main Question or Discussion Point

There is a 2D array of x and y positions of a vehicle measured at an interval of one second, e.g.:
x y
1, 5
1, 6
1.5, 6.8
...

I need to somehow quantify how a given driver approaches curves (i.e. driving style - does he/she drives aggressively or not). For this, I divided the problem into two sub-problems:

Step 1: Define curves by estimating angles
Step 2: Estimate the speed change or acceleration at these curves.

I am not sure that my approach is the best one. I would appreciate a link to some online resource where similar problem is discussed. I also appreciate any idea of how to evaluate a driving style at curves. Finally, I don't know how to perform Step 1, so any help is welcome.

## Answers and Replies

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mfb
Mentor
If your data points are dense enough, you can calculate velocity, acceleration and jerk (change of acceleration) all as differences between two adjacent values each. There are better approaches, but if you don't need them you can save work.
"driving style" and "aggressively or not" will need some mathematical representation to get evaluated.

@mfb: Thank you. Could you please provide some links or guidelines related to better approaches? The problem is that the data contains some hyperspace jumps. Also, I appreciate a lot you can share some ideas of how to quantitatively evaluate "driving style".

mfb
Mentor
Hyperspace jumps?

I think I would have to look at some actual data to say more.
Curve fitting is the general way you could do better than calculating differences, but then you need some models for the curves (e.g. something like that).

Hyperspace jumps?

I think I would have to look at some actual data to say more.
Curve fitting is the general way you could do better than calculating differences, but then you need some models for the curves (e.g. something like that).
Example of a hyperspace jump (measures are made at an interval of 1 second):
-580, 250
-600, 259
-1200,397 (here we have a jump of around 600 meters per second)
-1250,382

I suppose that my data is too complicated to be fitted with some analytical model, it contains multiple curves. Maybe it might be a good idea to smooth the data. I am, however, afraid that some important information like jerk can be lost after smoothing...

mfb
Mentor
Meters per second or meters?
A jump looks like a very rapid change in position (and speed?). Just find and ignore them.

Meters per second or meters?
A jump looks like a very rapid change in position (and speed?). Just find and ignore them.
Meters per second. Well, yes, currently I just find and clean these jumps. However, it would be interesting to know more details about the things you have mentioned in your first post (advanced math methods). Could you please give more details?

mfb
Mentor
See my second post.
It is hard to get more specific without more details of your problem.